$\displaystyle \sin \frac {2 \pi}3 = \pm \sin \frac {\pi}3$ and $\displaystyle \cos \frac {2 \pi}3 = \pm \cos \frac {\pi}3$. those values you should know. but how do we figure out the signs? we do that by finding out what quadrant the angle $\displaystyle \frac {2 \pi}3$ is in.

Remember the mnemonic, All Students Take Calculus

if it is in the first quad: sine is positive and cosine is positive
if it is in the second quad: sine is positive and cosine is negative
if it is in the third quad: sine is negative and cosine is negative
if it is in the fourth quad: sine is negative and cosine is positive

so, what's the answer?

Oct 2nd 2007, 05:12 PM

redpanda11

sin root 3/2,
cos -1/2?

Oct 2nd 2007, 05:23 PM

redpanda11

sin + pi/3, cos -pi/3

Oct 2nd 2007, 05:26 PM

Jhevon

Quote:

Originally Posted by redpanda11

sin root 3/2,
cos -1/2?

what? why is there sine and cosine in your answer? the answers are just numbers.

sorry!! i understand it to a certain extent but what if it's like tan 19pi/6 how do you know what quadrant it is in??

Oct 2nd 2007, 05:36 PM

Jhevon

Quote:

Originally Posted by redpanda11

sorry!! i understand it to a certain extent but what if it's like tan 19pi/6 how do you know what quadrant it is in??

you can keep adding or subtracting $\displaystyle 2 \pi$ if you don't like the size of the angle. you won't change it's value, you just change the number of revolutions to get there. so here, you would realize that $\displaystyle \frac {19 \pi}6 \equiv \frac {7 \pi}6$